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1/

Get a cup of coffee.

In this thread, I'll walk you through the importance of understanding *correlations* between bets.

For example, a portfolio of *correlated* stocks can have very different performance characteristics compared to a portfolio of *uncorrelated* stocks.

Get a cup of coffee.

In this thread, I'll walk you through the importance of understanding *correlations* between bets.

For example, a portfolio of *correlated* stocks can have very different performance characteristics compared to a portfolio of *uncorrelated* stocks.

2/

Imagine we put $100K into a stock.

In the next 1 year, the stock could go down 30% (our worst case scenario).

Or it could go up 50% (our best case scenario).

Or it could give us a return somewhere between these extremes.

Say all such returns are equally likely.

Imagine we put $100K into a stock.

In the next 1 year, the stock could go down 30% (our worst case scenario).

Or it could go up 50% (our best case scenario).

Or it could give us a return somewhere between these extremes.

Say all such returns are equally likely.

1/

Get a cup of coffee.

In this thread, I'll help you understand the concept of Half Life, and how it's relevant to investing.

Get a cup of coffee.

In this thread, I'll help you understand the concept of Half Life, and how it's relevant to investing.

2/

Imagine we have an investment opportunity.

If the investment goes well, we get to double our money.

But if it goes badly, we'll end up losing three fourths of it.

There's a 50/50 chance of either outcome.

The question: is this a good bet or not?

Imagine we have an investment opportunity.

If the investment goes well, we get to double our money.

But if it goes badly, we'll end up losing three fourths of it.

There's a 50/50 chance of either outcome.

The question: is this a good bet or not?

3/

A simple way to approach this question is to calculate the bet's "expectation".

For every $1 we bet, there are 2 possibilities:

1. The lucky case, where we double our money and end up with $2, and

2. The unlucky case, where we lose (3/4)'th to end up with just $0.25.

A simple way to approach this question is to calculate the bet's "expectation".

For every $1 we bet, there are 2 possibilities:

1. The lucky case, where we double our money and end up with $2, and

2. The unlucky case, where we lose (3/4)'th to end up with just $0.25.

1/

Get a cup of coffee.

In this thread, I'll walk you through the concept of "path dependence".

This plays such a key role in deciding so many financial outcomes.

And yet, most financial projections completely ignore it.

Get a cup of coffee.

In this thread, I'll walk you through the concept of "path dependence".

This plays such a key role in deciding so many financial outcomes.

And yet, most financial projections completely ignore it.

2/

Suppose we have $1M invested in an S&P 500 index fund.

Say, we leave this money untouched for the next 30 years.

If we get a steady 10% per year return over this period, we'll be left with ~$17M.

Not a bad result.

Suppose we have $1M invested in an S&P 500 index fund.

Say, we leave this money untouched for the next 30 years.

If we get a steady 10% per year return over this period, we'll be left with ~$17M.

Not a bad result.

3/

Of course, we probably won't get a *steady* 10% return every year.

Some years, we'll likely make more than 10%. Other years, we may even get a negative return and lose money.

It's all part of the game.

Of course, we probably won't get a *steady* 10% return every year.

Some years, we'll likely make more than 10%. Other years, we may even get a negative return and lose money.

It's all part of the game.

1/

Get a cup of coffee.

In this thread, I'll help you understand the basics of Binomial Thinking.

The future is always uncertain. There are many different ways it can unfold -- some more likely than others. Binomial thinking helps us embrace this view.

Get a cup of coffee.

In this thread, I'll help you understand the basics of Binomial Thinking.

The future is always uncertain. There are many different ways it can unfold -- some more likely than others. Binomial thinking helps us embrace this view.

2/

The S&P 500 index is at ~3768 today.

Suppose we want to predict where it will be 10 years from now.

Historically, we know that this index has returned ~10% per year.

If we simply extrapolate this, we get an estimate of ~9773 for the index 10 years from now:

The S&P 500 index is at ~3768 today.

Suppose we want to predict where it will be 10 years from now.

Historically, we know that this index has returned ~10% per year.

If we simply extrapolate this, we get an estimate of ~9773 for the index 10 years from now:

3/

What we just did is called a "point estimate" -- a prediction about the future that's a single number (9773).

But of course, we know the future is uncertain. It's impossible to predict it so precisely.

So, there's a sense of *false precision* in point estimates like this.

What we just did is called a "point estimate" -- a prediction about the future that's a single number (9773).

But of course, we know the future is uncertain. It's impossible to predict it so precisely.

So, there's a sense of *false precision* in point estimates like this.

1/

Get a cup of coffee.

Let's talk about the Birthday Paradox.

This is a simple exercise in probability.

But from it, we can learn so much about life.

About strategic problem solving.

About non-linear thinking -- convexity, concavity, S curves, etc.

So let's dive in!

Get a cup of coffee.

Let's talk about the Birthday Paradox.

This is a simple exercise in probability.

But from it, we can learn so much about life.

About strategic problem solving.

About non-linear thinking -- convexity, concavity, S curves, etc.

So let's dive in!

2/

Suppose we came across a "30 under 30" Forbes list.

The list features 30 highly accomplished people.

What are the chances that at least 2 of these 30 share the same birthday?

Same birthday means they were born on the same day (eg, Jan 5). But not necessarily the same year.

Suppose we came across a "30 under 30" Forbes list.

The list features 30 highly accomplished people.

What are the chances that at least 2 of these 30 share the same birthday?

Same birthday means they were born on the same day (eg, Jan 5). But not necessarily the same year.

3/

What if it was a "40 under 40" list?

Or a "50 under 50" list?

Or in general: if we put M people on a list, what are the chances that *some* 2 of them will share the same birthday?

What if it was a "40 under 40" list?

Or a "50 under 50" list?

Or in general: if we put M people on a list, what are the chances that *some* 2 of them will share the same birthday?